• Source: List of fractals by Hausdorff dimension

      • According to Benoit Mandelbrot, "A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension."
      Presented here is a list of fractals, ordered by increasing Hausdorff dimension, to illustrate what it means for a fractal to have a low or a high dimension.


      Deterministic fractals




      Random and natural fractals




      See also



      Fractal dimension
      Hausdorff dimension
      Scale invariance


      Notes and references




      Further reading


      Mandelbrot, Benoît (1982). The Fractal Geometry of Nature. W.H. Freeman. ISBN 0-7167-1186-9.
      Peitgen, Heinz-Otto (1988). Saupe, Dietmar (ed.). The Science of Fractal Images. Springer Verlag. ISBN 0-387-96608-0.
      Barnsley, Michael F. (1 January 1993). Fractals Everywhere. Morgan Kaufmann. ISBN 0-12-079061-0.
      Sapoval, Bernard; Mandelbrot, Benoît B. (2001). Universalités et fractales: jeux d'enfant ou délits d'initié?. Flammarion-Champs. ISBN 2-08-081466-4.


      External links


      The fractals on Mathworld
      Other fractals on Paul Bourke's website
      Soler's Gallery
      Fractals on mathcurve.com
      1000fractales.free.fr - Project gathering fractals created with various software
      Fractals unleashed
      IFStile - software that computes the dimension of the boundary of self-affine tiles

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